New York City Ballet’s spring season is six weeks long and the third and fourth weeks —May 2 through 14—showcase 21st-century choreography, i.e., works premiered in recent years. Justin Peck is represented on two different programs and Kyle Abraham has once more collaborated with the costume designer Giles Deacon: the ballet is titled Love Letter (on shuffle) and uses the music of James Blake. Gianna Reisen’s Play Time, which premiered last fall to music by Solange Knowles and wears glittery, somewhat Cubist costumes, has also come back. The program titled 21st-Century Choreography II presents new ballets by Alysa Pires and Christopher Wheeldon. The company’s 2023 Spring Gala is on May 4. —Laura Jacobs